Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
292 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15690881 | C2 | semidirect |
| 2. C2×#15690875 | C2 | semidirect |
| 3. C2×#15690874 | C2 | semidirect |
| 4. #20261710 | C2 | semidirect |
| 5. #20261709 | C2 | semidirect |
| 6. C2×#15690864 | C2 | semidirect |
| 22. C2×#13095501 | C4 | semidirect |
| 23. C2×#13095500 | C4 | semidirect |
| 24. C2×#13095496 | C4 | semidirect |
| 26. C2×SD16×C97 | C4 | semidirect |
| 120. C97 | #1975 | semidirect |
| 134. C2×SD16 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690881 | 2 |
| C2×#15690875 | 2 |
| C2×#15690874 | 2 |
| #20261710 | 2 |
| #20261709 | 2 |
| C2×#15690864 | 2 |
| C2×#15690831 | 2 |
| #1975 | 97 |